Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 9.1, Problem 3E
Pilates is a popular set of exercises for the treatment of individuals with lower back pain. The method has six basic principles: centering, concentration, control, precision, flow, and breathing. The article “Efficacy of the Addition of Modified Pilates Exercises to a Minimal Intervention in Patients with Chronic Low Back Pain: A Randomized Controlled Trial” (Physical Therapy, 2013: 309–321) reported on an experiment involving 86 subjects with nonspecific low back pain. The participants were randomly divided into two groups of equal size. The first group received just educational materials, whereas the second group participated in 6 weeks of Pilates exercises. The sample mean level of pain (on a scale from 0 to 10) for the control group at a 6-week follow-up was 5.2 and the sample mean for the treatment group was 3.1; both sample standard deviations were 2.3.
a. Does it appear that true average pain level for the control condition exceeds that for the treatment condition? Carry out a test of hypotheses using a significance level of .01 (the cited article reported statistical significance at this a, and a sample mean difference of 2.1 also suggests practical significance).
b. Does it appear that true average pain level for the control condition exceeds that for the treatment condition by more than 1? Carry out a test of appropriate hypotheses.
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Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the
0.05
level of significance, to support the claim that
μ
, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to
900…
Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of
900
Gy
(grays). (For comparison, humans cannot withstand more than
10
Gy
.) A study was conducted on a sample of
27
randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of
907
Gy
, with a sample standard deviation of
17
Gy
. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is approximately normally distributed.
Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the
0.05
level of significance, to support the claim that
μ
, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to
900…
Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of
1350
Gy
(grays). (For comparison, humans cannot withstand more than
10
Gy
.) A study was conducted on a sample of
18
randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of
1375
Gy
, with a sample standard deviation of
75
Gy
. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is approximately normally distributed.
Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the
0.05
level of significance, to support the claim that
μ
, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to
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Chapter 9 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 9.1 - An article in the November 1983 Consumer Reports...Ch. 9.1 - The National Health Statistics Reports dated Oct....Ch. 9.1 - Pilates is a popular set of exercises for the...Ch. 9.1 - Reliance on solid biomass fuel for cooking and...Ch. 9.1 - Persons having Reynauds syndrome are apt to suffer...Ch. 9.1 - An experiment to compare the tension bond strength...Ch. 9.1 - Is there any systematic tendency for part-time...Ch. 9.1 - Tensile-strength tests were carried out on two...Ch. 9.1 - The article Evaluation of a Ventilation Strategy...Ch. 9.1 - An experiment was performed to compare the...
Ch. 9.1 - The level of lead in the blood was determined for...Ch. 9.1 - The accompanying summary data on total cholesterol...Ch. 9.1 - A mechanical engineer wishes to compare strength...Ch. 9.1 - The level of monoamine oxidase (MAO) activity in...Ch. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.2 - Determine the number of degrees of freedom for the...Ch. 9.2 - Which way of dispensing champagne, the traditional...Ch. 9.2 - Suppose 1 and 2 are true mean stopping distances...Ch. 9.2 - Use the data of Exercise 19 to calculate a 95% CI...Ch. 9.2 - Quantitative noninvasive techniques are needed for...Ch. 9.2 - According to the article Modeling and Predicting...Ch. 9.2 - Fusible interlinings are being used with...Ch. 9.2 - Damage to grapes from bird predation is a serious...Ch. 9.2 - The accompanying data consists of prices () for...Ch. 9.2 - The article The Influence of Corrosion Inhibitor...Ch. 9.2 - Anorexia Nervosa (AN) is a psychiatric condition...Ch. 9.2 - As the population ages, there is increasing...Ch. 9.2 - The article Effect of Internal Gas Pressure on the...Ch. 9.2 - The article Flexure of Concrete Beams Reinforced...Ch. 9.2 - Refer to Exercise 33 in Section 7.3. The cited...Ch. 9.2 - The degenerative disease osteoarthritis most...Ch. 9.2 - The article The Effects of a Low-Fat, Plant-Based...Ch. 9.2 - Consider the pooled t variable T=(XY)(12)sp1m+1n...Ch. 9.2 - Prob. 35ECh. 9.3 - Consider the accompanying data on breaking load...Ch. 9.3 - Prob. 37ECh. 9.3 - Adding computerized medical images to a database...Ch. 9.3 - Scientists and engineers frequently wish to...Ch. 9.3 - Lactation promotes a temporary loss of bone mass...Ch. 9.3 - Antipsychotic drugs are widely prescribed for...Ch. 9.3 - Many freeways have service (or logo) signs that...Ch. 9.3 - Cushings disease is characterized by muscular...Ch. 9.3 - Prob. 44ECh. 9.3 - Torsion during hip external rotation (ER) and...Ch. 9.3 - Example 7.11 gave data on the modulus of...Ch. 9.3 - The article Slender High-Strength RC Columns Under...Ch. 9.3 - Prob. 48ECh. 9.4 - Consider the following two questions designed to...Ch. 9.4 - Recent incidents of food contamination have caused...Ch. 9.4 - It is well known that a placebo, a fake medication...Ch. 9.4 - Do teachers find their work rewarding and...Ch. 9.4 - Olestra is a fat substitute approved by the FDA...Ch. 9.4 - Teen Court is a juvenile diversion program...Ch. 9.4 - In medical investigations, the ratio = p1/p2 is...Ch. 9.4 - Sometimes experiments involving success or failure...Ch. 9.4 - Two different types of alloy, A and B, have been...Ch. 9.4 - Prob. 58ECh. 9.5 - Obtain or compute the following quantities: a....Ch. 9.5 - Give as much information as you can about the...Ch. 9.5 - Prob. 61ECh. 9.5 - Prob. 62ECh. 9.5 - Toxaphene is an insecticide that has been...Ch. 9.5 - The following observations are on time (h) for a...Ch. 9.5 - The article Enhancement of Compressive Properties...Ch. 9.5 - Prob. 66ECh. 9 - The accompanying summary data on compression...Ch. 9 - The article Supervised Exercise Versus Non-...Ch. 9 - Is the response rate for questionnaires affected...Ch. 9 - Shoveling is not exactly a high-tech activity, but...Ch. 9 - The article Quantitative MRI and Electrophysiology...Ch. 9 - The following summary data on bending strength...Ch. 9 - Prob. 73SECh. 9 - The derailment of a freight train due to the...Ch. 9 - Prob. 75SECh. 9 - Prob. 76SECh. 9 - Information about hand posture and forces...Ch. 9 - Prob. 78SECh. 9 - The article The Accuracy of Stated Energy Contents...Ch. 9 - Arsenic is a known carcinogen and poison. The...Ch. 9 - Prob. 81SECh. 9 - Acrylic bone cement is commonly used in total...Ch. 9 - In an experiment to compare bearing strengths of...Ch. 9 - Prob. 84SECh. 9 - An experimenter wishes to obtain a CI for the...Ch. 9 - Prob. 86SECh. 9 - Prob. 87SECh. 9 - The paper Quantitative Assessment of Glenohumeral...Ch. 9 - Prob. 89SECh. 9 - Prob. 90SECh. 9 - Prob. 91SECh. 9 - Prob. 92SECh. 9 - The article Evaluating Variability in Filling...Ch. 9 - Prob. 94SECh. 9 - Prob. 95SE
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